House edge as school arithmetic

An American layout has 38 pockets: numbers 1 to 36 plus 0 and 00. Stake one unit on red: 18/38 win paths, 20/38 lose paths. Expected value is −2/38, written −0.0526 in the Dartmouth probability text — a 5.26% edge. Cycle a hundred units through that bet and the long-run cost sits a little above five units.

A European layout has 37 pockets. The same red bet wins in 18 of 37 cases. Straight-up numbers still pay 35 to 1 while true odds are 1/37; even-money colours pay 1 to 1 (Massachusetts official roulette rules). Expected loss per unit is about 0.027 — a 2.7% edge. Same game family, one pocket less; if you play roulette, prefer the single-zero build.

Carry the edge as a comparison tool, not a superstition filter. Prefer the cheaper ruleset when two tables offer the same entertainment — single-zero over double-zero, full-payout blackjack over reduced naturals. Ignore staking "systems" that rearrange loss paths. When a bonus asks you to cycle large volumes, multiply that volume by the edge of the games that actually clear wagering; the product is often larger than the headline credit. Country editions explain local tables and rails (Canada, United States); the arithmetic on this page stays the same everywhere.

Each round is independent; longer play pulls results toward the edge. Doubling after losses reshapes ruin, not expectation. Compare titles instead: blackjack with basic strategy sits far below roulette, while bonus wagering can cost more than a fraction of a percent of edge ever will.